Deep learning has shown its superiority to traditional machine learning methods in various fields, and in general, its success depends on the availability of large amounts of reliable data. However, in some scientific fields such as materials science, such big data is often expensive or even impossible to collect. Thus given relatively small datasets, most of data-driven methods are based on traditional machine learning methods, and it is challenging to apply deep learning for many tasks in these fields. In order to take the advantage of deep learning even for small datasets, a domain knowledge integration approach is proposed in this work. The efficacy of the proposed approach is tested on two materials science datasets with different types of inputs and outputs, for which domain knowledge-aware convolutional neural networks (CNNs) are developed and evaluated against traditional machine learning methods and standard CNN-based approaches. Experiment results demonstrate that integrating domain knowledge into deep learning can not only improve the model's performance for small datasets, but also make the prediction results more explainable based on domain knowledge.